Optical device

ABSTRACT

According to one embodiment, an optical device includes a first mirror, a second mirror, and a first member. The first mirror has a first planar surface. The second mirror is spaced from the first mirror in a first direction crossing the first planar surface. The second mirror has a concave surface including a first region and a second region around the first region. First distance between the first region and the first planar surface in the first direction is longer than second distance between the second region and the first planar surface in the first direction. The first distance is half or less of curvature radius of the concave surface. The first member is light transmissive and solid. The first member includes a first portion provided between the first mirror and the second mirror. The first portion is in contact with the first planar surface and the concave surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromJapanese Patent Application No. 2017-180006, filed on Sep. 20, 2017; theentire contents of which are incorporated herein by reference.

FIELD

Embodiments described herein relate generally to a optical device.

BACKGROUND

There is known an optical device with two mirrors opposed to each other.An optical device with high performance is desired.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 and 2A to 2C are schematic views illustrating an optical deviceaccording to an embodiment;

FIGS. 3 to 5 are graphs illustrating the characteristics of the opticaldevice;

FIGS. 6A and 6B are schematic views illustrating an alternative opticaldevice according to the embodiment;

FIG. 7 is a schematic sectional view illustrating an optical deviceaccording to a first practical example;

FIGS. 8A and 8B are schematic views illustrating an optical deviceaccording to a second practical example; and

FIGS. 9A, 9B, and 10A to 10C are schematic views illustrating an opticaldevice according to the embodiment.

DETAILED DESCRIPTION

According to one embodiment, an optical device includes a first mirror,a second mirror, and a first member. The first mirror has a first planarsurface. The second mirror is spaced from the first mirror in a firstdirection crossing the first planar surface. The second mirror has aconcave surface including a first region and a second region around thefirst region. First distance between the first region and the firstplanar surface in the first direction is longer than second distancebetween the second region and the first planar surface in the firstdirection. The first distance is half or less of curvature radius of theconcave surface. The first member is light transmissive. The firstmember is solid. The first member includes a first portion providedbetween the first mirror and the second mirror. The first portion is incontact with the first planar surface and the concave surface.

Embodiments of the invention will now be described with reference to thedrawings.

The drawings are schematic or conceptual; and the relationships betweenthe thicknesses and widths of portions, the proportions of sizes betweenportions, etc., are not necessarily the same as the actual valuesthereof. The dimensions and/or the proportions may be illustrateddifferently between the drawings, even in the case where the sameportion is illustrated.

In the drawings and the specification of the application, componentssimilar to those described thereinabove are marked with like referencenumerals, and a detailed description is omitted as appropriate.

FIGS. 1 and 2A to 2C are schematic views illustrating an optical deviceaccording to an embodiment.

FIG. 2A is a sectional view taken along line A1-A2 of FIG. 1. FIG. 2B isa sectional view taken along line A3-A4 of FIG. 1. FIG. 1 is a plan viewas viewed in the direction of arrow A5 of FIG. 2A. FIG. 2C is a planview of the second mirror as viewed in the direction of arrow A6 of FIG.2A.

As shown in FIGS. 1 and 2A to 2C, the optical device 110 according tothe embodiment includes a first mirror 10, a second mirror 20, a firstmember 31, a first prism 41, a second prism 42, and a support part 90.

The first mirror 10 has a first planar surface 11P. The second mirror 20is spaced from the first mirror 10 in a first direction crossing thefirst planar surface 11P. The second mirror 20 has a concave surface21C. The concave surface 21C is opposed to the first planar surface 11P.The first mirror 10 is provided between the second mirror 20 and thesupport part 90.

The first direction lies along e.g. the Z-axis direction shown inFIG. 1. One direction perpendicular to the Z-axis direction is referredto as X-axis direction. The direction perpendicular to the X-axisdirection and the Z-axis direction is referred to as Y-axis direction. Asecond direction lies along e.g. the X-axis direction. A third directionlies along e.g. the Y-axis direction.

The following describes the case where the first direction, the seconddirection, and the third direction lie along the Z-axis direction, theX-axis direction, and the Y-axis direction, respectively.

As shown in FIG. 2C, the concave surface 21C includes a first region 21a and a second region 21 b around the first region 21 a. As shown inFIGS. 2A and 2B, the first distance D1 along the Z-axis directionbetween the first region 21 a and the first planar surface 11P is longerthan the second distance D2 along the Z-axis direction between thesecond region 21 b and the first planar surface 11P. For instance, thefirst region 21 a crosses the axis passing through the center in theX-axis direction and the Y-axis direction of the second mirror 20. Thisaxis lies along the Z-axis direction.

For instance, the length L1 in the X-axis direction of the first mirror10 is longer than the length L2 in the X-axis direction of the secondmirror 20. For instance, the length L3 in the Y-axis direction of thefirst mirror 10 is longer than the length L4 in the Y-axis direction ofthe second mirror 20. The length L1 is longer than the length L3. Thelength L2 is e.g. equal to the length L4. The length L2 may be differentfrom the length L4.

The first member 31 is light transmissive. The first member 31 is solid.The first member 31 includes a first portion 31 a located between thefirst mirror 10 and the second mirror 20 in the Z-axis direction. Thefirst portion 31 a is in contact with the first planar surface 11P andthe concave surface 21C.

The first member 31 further includes e.g. a second portion 31 b. Thedirection from the first portion 31 a to the second portion 31 b crossesthe Z-axis direction. The first member 31 may further include a thirdportion 31 c. The first portion 31 a is located between the secondportion 31 b and the third portion 31 c in the X-axis direction. Thesecond portion 31 b and the third portion 31 c do not overlap the secondmirror 20 in the Z-axis direction.

For instance, the length L6 along the Z-axis direction of the secondportion 31 b is shorter than the length L5 along the Z-axis direction ofthe first portion 31 a. For instance, the length L7 along the Z-axisdirection of the third portion 31 c is shorter than the length L5.

In this example, the length L8 in the X-axis direction of the firstmember 31 is equal to the length L1. The length L9 in the Y-axisdirection of the first member 31 is shorter than the length L3. Thelength L8 is longer than the length L2. The length L9 is longer than thelength L4.

The first prism 41 and the second prism 42 are light transmissive. Thefirst prism 41 and the second prism 42 are spaced from the second mirror20 in the X-axis direction. The direction from part of the secondportion 31 b to the first prism 41 lies along the Z-axis direction. Thedirection from part of the third portion 31 c to the second prism 42lies along the Z-axis direction.

For instance, light is incident on the first prism 41. Then, the lightis guided from the second portion 31 b to the first portion 31 a. Partof the light is guided from the first portion 31 a to the third portion31 c and emitted from the second prism 42. The optical device 110functions as an optical resonator. Here, “light” includes not onlyvisible light, but also electromagnetic waves of wavelengths in otherregions. For instance, “light” includes electromagnetic waves having awavelength of 200 nm or more and 1 mm or less and visible light.

The first mirror 10 contains e.g. at least one selected from the firstgroup consisting of TiO₂, Ta₂O₃, SiO₂, MgF₂, TiO₃, and Nb₂O₅. The firstmirror 10 may include a plurality of layers. Each of these layerscontains at least one selected from the first group. The second mirror20 contains e.g. at least one selected from the second group consistingof TiO₂, Ta₂O₃, SiO₂, MgF₂, TiO₃, and Nb₂O₅. The second mirror 20 mayinclude a plurality of layers. Each of these layers contains at leastone selected from the second group.

The first member 31 contains e.g. at least one selected from the groupconsisting of Y₂SiO₅, LF₃, SiO₂, and C. The first member 31 may containat least one selected from the group, and a rare-earth ion. Therare-earth ions are e.g. dispersed in the at least one material.

The first prism 41 and the second prism 42 contain e.g. at least oneselected from the group consisting of BK7 and fused silica. The supportpart 90 contains e.g. at least one selected from the group consisting ofSiO₂, Si, and glass.

The inventors have discovered that the performance of the optical device110 can be improved when the optical device 110 includes the followingconfiguration.

The concave surface 21C is e.g. spherical. The concave surface 21C liesalong e.g. part of a sphere. For instance, the curvature of the concavesurface 21C in a cross section including the X-axis direction and theZ-axis direction is equal to the curvature of the concave surface 21C ina cross section including the Y-axis direction and the Z-axis direction.The first distance D1 is 0.5 times or less the curvature radius of theconcave surface 21C. Preferably, the first distance D1 is 0.3 times orless the curvature radius of the concave surface 21C. More preferably,the first distance D1 is 0.1 times or less the curvature radius of theconcave surface 21C.

The concave surface 21C may not be spherical.

Application of one of the above configurations can improve e.g. thecharacteristic of the optical device. This characteristic is e.g. acharacteristic in the case of using the coupling between the resonatormode occurring in the optical device and the physical system coupled tothe resonator mode.

It is considered that this effect occurs for the following reason.

FIGS. 3 to 5 are graphs illustrating the characteristics of the opticaldevice.

When the first distance D1 (resonator length L) is changed, in theresonator mode of the gaussian mode occurring in the optical device 110(resonator), FIG. 3 shows the mode waist radius ω₀ of the TEM₀₀ modeplotted with respect to L. The wavelength in a vacuum of the resonatormode is denoted by λ. The refractive index in the resonator is denotedby n_(ri). The relationship represented by the following equation 1exists among the mode waist radius ω₀, the curvature radius R of theconcave surface 21C, the resonator length L, λ, and n_(ri). It isassumed that the anisotropy of the refractive index in the resonator issubstantially absent, or negligible.

$\begin{matrix}{\omega_{0} = {\left( \frac{\lambda}{\pi \; n_{ri}} \right)^{\frac{1}{2}}\left\{ {\left( {R - L} \right)L} \right\}^{\frac{1}{4}}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

The resonator mode (TEM₀₀ mode) of this resonator is coupled to thephysical system included therein with a coupling strength g throughoptical transition of transition angular frequency ω_(a)=2πcn_(ri)/λ (c:speed of light in a vacuum) of the physical system.

g depends on the position in the resonator mode. This is represented bythe following equation 2 using the spatial distribution Ψ(r) of theelectric field amplitude of the resonator mode normalized so that itsmaximum is 1. g₀ included in equation 2 is represented by the followingequation 3.

$\begin{matrix}{g = {g_{0}{\psi \left( \overset{\rightarrow}{r} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack \\{g_{0} = {\frac{\mu}{n_{ri}}\sqrt{\frac{\omega_{a}}{2\hslash \; ɛ_{0}V}}}} & \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack\end{matrix}$

μ is the transition dipole moment of the transition of the physicalsystem. ℏ is the Dirac constant.

ε₀ is the dielectric constant of a vacuum. V is referred to as modevolume and corresponds to the volume of the distribution region ofphotons of the resonator mode. V is represented by the followingequation 4 using Ψ(r).

V=∫|ψ({right arrow over (r)})|² d ³ {right arrow over (r)}  [Equation 4]

Next, consider the critical atom number (N₀) of this physicalsystem/resonator mode coupled system. N₀ serves as a figure of merit invarious techniques, devices, and measurement methods using such aphysical system/resonator mode coupled system. In general, a smaller N₀indicates high performance of the physical system/resonator mode coupledsystem. N₀ is represented by the following equation 5.

$\begin{matrix}{N_{0} = \frac{k\; \Gamma}{g^{2}}} & \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack\end{matrix}$

κ is the relaxation rate of the resonator. Γ is the relaxation rate ofthe physical system. From equation 5, it is found that smaller N₀ can beobtained by making g larger. From equation 2, it is found that larger gcan be obtained by making g₀ larger. From equation 3, it is found thatlarger g₀ can be obtained by making V smaller.

There is known a Fabry-Perot resonator in which two mirror surfaces areopposed to hold photons in the resonator only by reflection at themirror surfaces. When the mode waist radius is narrowed to wavelengthorder, the mode is shaped like a circular cone or hourglass rather thana circular cylinder.

Even in this case, the mode volume V is represented by the followingequation 6 using the mode waist radius ω₀ and the resonator length L.

V=¼πω₀ ² L  [Equation 6]

From this equation 6, it is found that for smaller ω₀, V is smaller, andN₀ can be made smaller. It is considered that this can improve theperformance of techniques and devices using the physicalsystem/resonator mode coupled system. Thus, for instance, a physicalsystem/resonator mode coupled system with smaller ω₀ is considered.

As shown in FIG. 3, ω₀ is smaller in the region of L nearly equal to R(L≈R region) and the region of L close to zero (L≈0 region). Forinstance, in order to make N₀ particularly small, it is considered touse the L≈R region for the following reason. As ω₀ becomes smaller, Vbecomes smaller, and g₀ sharply becomes larger. However, it isconsidered that the resonator length and the relaxation rate of thephysical system undergo small or no change. From equation 5, it islikely to be anticipated that N₀ becomes smaller. The physical system iseasily inserted into the optical device. It is easy to applymanipulation light for manipulating the physical system.

On the other hand, in the L≈0 region, for instance, making g₀ larger bymaking V smaller also increases the optical loss (the number of photonslost per unit time) such as transmission, scattering, and absorptionoccurring at the mirror. Thus, it is not evident whether N₀ can be madesmaller.

For instance, 29 resonators are fabricated. These resonators have anequal curvature radius R of the concave surface 21C and are different inthe resonator length L, e.g., L_(i)=i×R/30 (i=1, 2, . . . , 29). Theseresonators are monolithically fabricated by polishing the surface of thefirst member 31 that transmits light of the wavelength of the resonatormode. For each resonator, the dissipation K of the resonator ismeasured. κ_(i) can be measured by observing the spectral width of theresonator mode.

κ_(i) thus measured and L_(i) are used to calculate N_(0i)′ representedby the following equation 7. This is graphically depicted in FIG. 4.Furthermore, a hollow resonator is fabricated from two mirrors having asimilar reflectance. The graph obtained similarly is shown in FIG. 5.

N _(0i)′=κ_(i) L _(i)√{square root over ((R−L _(i))L _(i))}  [Equation7]

The critical atom number N₀ of the resonators is represented by equation5. When these resonators include a physical system, N₀ is minimized atthe position of the mode waist where the coupling between the physicalsystem and the resonator mode is maximized (the position where Ψ(r)=1).From equations 1, 2, 3, 5, and 6, N₀ at this position is represented bythe following equation 8. C₁ included in equation 8 is represented bythe following equation 9.

$\begin{matrix}{N_{0} = {\frac{k\; \Gamma}{g_{0}^{2}} = {C_{1}\kappa \; L\sqrt{\left( {R - L} \right)L}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \\{C_{1} = \frac{\hslash \; ɛ_{0}n_{ri}\lambda \; \Gamma}{2{\mu \;}^{2}\omega_{a}}} & \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack\end{matrix}$

The critical atom number N_(0i) at the mode waist represents theperformance of each of the 29 resonators. The critical atom numberN_(0i) is represented by the following equation 10 from the constant C₁taking the same value for the resonators, L_(i) being different for eachresonator, and κ_(i) being different for each resonator and obtained bymeasurement. The constant C₁ is the same value for the resonators. L_(i)and κ_(i) are different for each resonator.

N _(0i) =C ₁κ_(i) L _(i)√{square root over ((R−L _(i))L_(i))}  [Equation 10]

Equation 10 is represented as the following equation 11.

N _(0i) =C ₁ N _(0i)′  [Equation 11]

That is, N_(0i) is a constant multiple of N_(0i)′. The inventors havefound from FIG. 4 that N_(0i) can be made smaller more easily in the L≈0region than in the L≈R region. With R being fixed, the difference (L−R)between L and R in the region of the first distance D1 (the resonatorlength L) longer than R/2 (including the L≈R region) is denoted by d1. Lin the region of the first distance D1 (the resonator length L) shorterthan R/2 (including the L≈0 region) is denoted by d2. Then, fromequation 1, when d1=d2, the two resonators have an equal mode waistradius ω₀. However, N_(0i) is smaller in the region of the resonatorlength L shorter than R/2.

FIG. 5 shows that the superiority in the region of the resonator lengthL shorter than R/2 results from photon loss such as absorption andscattering occurring in the medium in the resonator. This is because thehollow resonator does not exhibit the superiority as shown in FIG. 5. Itis considered that such superiority of the L≈0 region to the L≈R regionoccurs for the following reason.

The process in which photons are lost from the resonator includes photonloss such as transmission, scattering, and absorption occurring at themirror and photon loss such as absorption and scattering occurring inthe medium in the resonator. The former is inversely proportional to theresonator length L. The latter does not depend on the resonator length Lif the medium is uniform. The former and latter photon losses aredenoted by C₂/L and C₃, respectively, using two constants. In this case,the relaxation rate κ of the resonator is represented by the followingequation 12.

$\begin{matrix}{\kappa = {\frac{C_{2}}{L} + C_{3}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack\end{matrix}$

Substituting this κ into equation 8 yields the following equation 13.

N ₀ =C ₁(C ₂ +C ₃)√{square root over ((R−L)L)}  [Equation 13]

This equation 13 represents a function indicating the behavior of thegraph of FIG. 4. Equation 13 also indicates that for larger photon loss(C₃) such as absorption and scattering occurring in the medium in theresonator, N₀ has a larger difference between the region of theresonator length L longer than R/2 and the region of the resonatorlength L shorter than R/2. Equation 13 also indicates that shorter L canreduce the influence of the photon loss (C₃) such as absorption andscattering occurring in the medium in the resonator.

Use of the physical system/resonator coupled system in the region of theresonator length L shorter than R/2 is also advantageous tominiaturization of the optical device 110. In particular, use of thephysical system/resonator coupled system in the L≈0 region isadvantageous to miniaturization of the optical device 110. In theoptical device 110 according to the embodiment, the mode waist ispreferably 100 μm or less. Preferably, the optical device 110 accordingto the embodiment has a resonator mode of the gaussian mode. Preferably,the first member 31 has a propagation mode traversing the optical axisof the resonator mode.

FIGS. 6A and 6B are schematic views illustrating an alternative opticaldevice according to the embodiment.

FIG. 6A is a plan view. FIG. 6B is a sectional view taken along a planeincluding the X-axis direction and the Z-axis direction.

As shown in FIGS. 6A and 6B, the optical device 120 includes a secondmember 32, a third member 33, a first support part 91, and a secondsupport part 92.

The first mirror 10 is provided between the first member 31 and thefirst support part 91. The second support part 92 is provided around thefirst support part 91. The direction from the first support part 91 tothe second support part 92 lies along the X-axis direction or the Y-axisdirection. The second support part 92 is in contact with the firstsupport part 91. The second support part 92 is fixed to the firstsupport part 91 with e.g. an adhesive 95.

The second member 32 and the third member 33 are light transmissive. Thesecond member 32 and the third member 33 are solid. The first member 31is provided between the second member 32 and the third member 33 in theX-axis direction.

Also in the optical device 120, the first distance between the firstregion 21 a and the first planar surface 11P is longer than the seconddistance between the second region 21 b and the first planar surface11P. The first distance is 0.5 times or less the curvature radius of theconcave surface 21C.

Alternatively, the first distance is equal to or less the focal lengthof the concave surface 21C.

First Practical Example

FIG. 7 is a schematic sectional view illustrating an optical deviceaccording to a first practical example.

The optical device 131 shown in FIG. 7 includes a first support part 91,a first mirror 10, a second mirror 20, and a first member 31. The firstsupport part 91 is a substrate (e.g. fused silica substrate). The firstmirror 10 and the second mirror 20 include a plurality of layers. Eachof these layers contains dielectric. The first member 31 is a singlecrystal of Y₂SiO₅.

This optical device 131 is fabricated e.g. as follows.

For instance, a first substrate (fused silica substrate) shaped like acircular column of radius 1.2 mm and height 3 mm is prepared. This firstsubstrate has a planar part. A dielectric multilayer film is formed onthe planar part. The transmittance of the dielectric multilayer film at606 nm is 1×10⁻³. A thin single-crystal plate is bonded in opticalcontact onto this dielectric multilayer film. This single-crystal plateis made of Y₂SiO₅ crystal. The dielectric multilayer film is locatedbetween this single-crystal plate and the first substrate. For instance,the B-axis of the bonded single crystal is perpendicular to the contactsurface of the single-crystal plate and the dielectric multilayer film.

The surface on the opposite side from the bonding surface of thesingle-crystal plate is polished like a sphere of curvature radius 10mm. The center of the sphere is located on the central axis CA of thefirst substrate shaped like a circular column. The central axis CA is astraight line passing through the center of the circle of the topsurface of the first substrate and the center of the circle of thebottom surface of the first substrate. The single-crystal plate ispolished so that the thickness of the single-crystal plate on thiscentral axis CA is 100 μm. The aforementioned thickness corresponds tothe thickness of the thickest portion of the single-crystal plate. Adielectric multilayer film is formed on the sphere of the single-crystalplate. For instance, the transmittance of the dielectric multilayer filmat 606 nm is 1.5×10⁻⁴. This dielectric multilayer film is formed in aregion having a radius of approximately 1 mm about the intersectionpoint of the sphere and the central axis CA. Thus, an optical device ofcurvature radius R=10 mm and resonator length L (first distance D1)=100μm is fabricated.

On the other hand, like the foregoing, an optical device with thethickness of the single-crystal plate on CA being 9.9 mm is fabricated.This thickness corresponds to the thickness of the thickest part of thesingle-crystal plate. This optical device has curvature radius R=10 mmand resonator length L (first distance D1)=9.9 mm.

For these two optical devices, the spectral width of the resonator modenear 606 nm is observed. The dissipation of each resonator is measured.N_(0i)′ represented by equation 7 is determined.

N_(0i)′ of the optical device of resonator length L=100 μm is referredto as first value V1. N_(0i)′ of the optical device of resonator lengthL=9.9 mm is referred to as second value V2. This yields V1/V2=0.3. Themode waist is approximately 10 μm in each of the optical device ofresonator length L=100 μm and the optical device of resonator lengthL=9.9 mm. This result indicates the following for the optical devicefilled inside with a solid material having absorption or scattering. Theoptical device of L<R/2 has better performance in terms of critical atomnumber N₀ than the optical device of L>R/2.

Second Practical Example

FIGS. 8A and 8B are schematic views illustrating an optical deviceaccording to a second practical example.

FIG. 8A is a plan view. FIG. 8B is a sectional view.

The optical device 132 shown in FIGS. 8A and 8B further includes e.g. asecond member 32 and a third member 33 compared with the optical device131.

This optical device 132 is fabricated as follows.

For instance, a second substrate (fused silica substrate) of 3 mm×10mm×3 mm is prepared. A hole shaped like a circular cylinder of radius1.2 mm is made in this second substrate. The optical device 131according to the first practical example of resonator length L=100 μm isinserted in this hole. In the optical device 131, the first mirror 10 iscomposed of a dielectric multilayer film. The optical device 131 and theoptical device 132 are aligned in position so that the surface on thespherical mirror side of this dielectric multilayer film is flush withthe first surface of 3 mm×10 mm of the second substrate. The secondsurface of the second substrate is bonded with an adhesive 95 to theside surface of the first substrate at at least one location. The secondsurface of the second substrate is a surface on the opposite side fromthe first surface. In this practical example, the first member containsPr³⁺ ions of 10⁻⁴ at %. That is, one of 10⁶ Y³⁺ ions contained in theY₂SiO₅ single crystal is replaced by a Pr³⁺ ion.

A Y₂SiO₅ target is sputtered using a mask to form a second member 32 anda third member 33 on the first surface of the second substrate. Thesecond member 32 and the third member 33 function as a ridge opticalwaveguide. This optical waveguide has a width of 10 μm and a thicknessof 5 μm. This optical waveguide is connected to the side surface of thefirst member 31 so that the propagation direction is orthogonal to thesymmetry axis of the resonator mode. Furthermore, a first prism 41 and asecond prism 42 are provided in order to introduce light to the opticalwaveguide. A refractive index change may be provided near the bondingportion of the first member 31 and the second member 32, near thebonding portion of the first member 31 and the third member 33, or inthe first member 31. Thus, for instance, a GRIN lens structure isformed. By this lens structure, the light introduced into the opticaldevice 131 may be converged to the site occupied by the physical systemcoupled to the resonator mode. In this practical example, the D₂-axis ofY₂SiO₅ constituting the first member 31 and containing Pr³⁺ ions isparallel to the plane of the first substrate and orthogonal to thepropagation direction of the waveguide. That is, the D₂-axis lies alonge.g. the Y-axis direction. This optical device is put in a cryostat andcooled to 4 K. In this state, the angular frequency of the resonatormode near 606 nm resonating with Pr³⁺ ions contained in Y₂SiO₅ isdenoted by ω_(c). Weak light of angular frequency ω_(c) is coupled tothe resonator mode. While monitoring transmission light from thisresonator, light of ω_(c)−27.5 MHz and ω_(c)−26.7 MHz with thepolarization direction being parallel to the D₂-axis is applied from thewaveguide. Then, the transmission light intensity decreases. Thus, thestate of Pr³⁺ ions constituting the physical system coupled to theresonator mode can be effectively manipulated by external lightintroduced using the waveguide.

FIGS. 9A, 9B, and 10A to 10C are schematic views illustrating an opticaldevice according to the embodiment.

FIG. 10A is a sectional view taken along line A7-A8 of FIG. 9A. FIG. 10Bis a sectional view taken along line A9-A10 of FIG. 9A. FIG. 9A is aplan view as viewed in the direction of arrow A11 of FIG. 10A. FIG. 9Bis a plan view of the first mirror as viewed in the direction of arrowA11. FIG. 10C is a plan view of the second mirror as viewed in thedirection of arrow A12 of FIG. 10A.

In the optical device 140, the first mirror 10 has a first concavesurface 11C. The first concave surface 11C includes a first region 11 aand a second region 11 b around the first region 11 a.

The second mirror 20 has a second concave surface 22C. The secondconcave surface 22C includes a third region 22 c and a fourth region 22d around the third region 22 c. For instance, the axis passing throughthe center in the X-axis direction and the Y-axis direction of thesecond mirror 20 crosses the first region 11 a and the third region 22c. This axis lies along e.g. the Z-axis direction. The direction fromthe first region 11 a to the third region 22 c lies along the Z-axisdirection. The direction from the second region 11 b to the fourthregion 22 d lies along the Z-axis direction. The first member 31includes a first portion 31 a in contact with the first concave surface11C and the second concave surface 22C.

The first distance D1 in the Z-axis direction between the first region11 a and the third region 22 c is longer than the second distance D2 inthe Z-axis direction between the second region 11 b and the fourthregion 22 d. The first distance D1 is 0.5 times or less the sum of thecurvature radius of the first concave surface 11C and the curvatureradius of the second concave surface 22C. Preferably, the first distanceD1 is 0.3 times or less the sum of the curvature radius of the firstconcave surface 11C and the curvature radius of the second concavesurface 22C. More preferably, the first distance D1 is 0.1 times or lessthe sum of the curvature radius of the first concave surface 11C and thecurvature radius of the second concave surface 22C.

The first concave surface 11C and the second concave surface 22C may notbe spherical.

Thus, the performance of the optical device 140 can be improved. Forinstance, the characteristics of the optical device can be improved.

The embodiments described above can provide an optical device capable ofimproving the performance.

In the specification of the application, “perpendicular” and “parallel”refer to not only strictly perpendicular and strictly parallel but alsoinclude, for example, the fluctuation due to manufacturing processes,etc. It is sufficient to be substantially perpendicular andsubstantially parallel.

Hereinabove, embodiments of the invention are described with referenceto specific examples. However, the invention is not limited to thesespecific examples. For example, one skilled in the art may similarlypractice the invention by appropriately selecting specificconfigurations of components included in the optical device such as themirror, the first member, the second member, the third member, theprism, the support part, etc., from known art; and such practice iswithin the scope of the invention to the extent that similar effects canbe obtained.

Further, any two or more components of the specific examples may becombined within the extent of technical feasibility and are included inthe scope of the invention to the extent that the purport of theinvention is included.

Moreover, all optical devices practicable by an appropriate designmodification by one skilled in the art based on the optical devicesdescribed above as embodiments of the invention also are within thescope of the invention to the extent that the spirit of the invention isincluded.

Various other variations and modifications can be conceived by thoseskilled in the art within the spirit of the invention, and it isunderstood that such variations and modifications are also encompassedwithin the scope of the invention.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the invention.

What is claimed is:
 1. An optical device comprising: a first mirrorhaving a first planar surface; a second mirror spaced from the firstmirror in a first direction crossing the first planar surface, thesecond mirror having a concave surface including a first region and asecond region around the first region, first distance between the firstregion and the first planar surface in the first direction being longerthan second distance between the second region and the first planarsurface in the first direction, and the first distance being half orless of curvature radius of the concave surface; and a first memberbeing light transmissive, being solid, and including a first portionprovided between the first mirror and the second mirror, the firstportion being in contact with the first planar surface and the concavesurface.
 2. The device according to claim 1, wherein the first memberfurther includes a second portion, direction from the first portion tothe second portion crosses the first direction, and the second portiondoes not overlap the second mirror in the first direction.
 3. The deviceaccording to claim 1, wherein the first member further includes a secondportion and a third portion, the first portion is located between thesecond portion and the third portion in a second direction crossing thefirst direction, and the second portion and the third portion do notoverlap the second mirror in the first direction.
 4. The deviceaccording to claim 3, wherein length along the first direction of atleast part of the first portion is longer than length along the firstdirection of the second portion and longer than length along the firstdirection of the third portion.
 5. The device according to claim 3,further comprising: a first prism, wherein the first prism is spacedfrom the second mirror in the second direction, and the first prismoverlaps part of the second portion in the first direction.
 6. Thedevice according to claim 5, wherein direction from part of the firstmirror to the first prism lies along the first direction.
 7. The deviceaccording to claim 1, further comprising: a translucent second member;and a translucent third member, wherein the first member is locatedbetween the second member and the third member in a second directioncrossing the first direction, and the second member and the third memberdo not overlap the second mirror in the first direction.
 8. The deviceaccording to claim 7, wherein length along the first direction of atleast part of the first member is longer than length along the firstdirection of the second member and longer than length along the firstdirection of the third member.
 9. The device according to claim 7,further comprising: a first prism, wherein the first prism is spacedfrom the second mirror in the second direction, and the first prismoverlaps part of the second member in the first direction.
 10. Thedevice according to claim 9, wherein direction from part of the firstmirror to the first prism lies along the first direction.
 11. The deviceaccording to claim 1, wherein the first mirror contains at least oneselected from the group consisting of TiO₂, Ta₂O₃, SiO₂, MgF₂, TiO₃, andNb₂O₅.
 12. The device according to claim 1, wherein the second mirrorcontains at least one selected from the group consisting of TiO₂, Ta₂O₃,SiO₂, MgF₂, TiO₃, and Nb₂O₅.
 13. The device according to claim 1,wherein the first member contains at least one selected from the groupconsisting of Y₂SiO₅, LF₃, SiO₂, and C.
 14. An optical devicecomprising: a first mirror having a first concave surface including afirst region and a second region provided around the first region; asecond mirror spaced from the first mirror in a first direction, thesecond mirror having a second concave surface including a third regionand a fourth region provided around the third region, first distancebetween the first region and the third region in the first directionbeing longer than second distance between the second region and thefourth region in the first direction, and the first distance being 0.5times or less of sum of curvature radius of the first concave surfaceand curvature radius of the second concave surface; and a first memberbeing light transmissive, being solid, and including a first portionprovided between the first mirror and the second mirror, the firstportion being in contact with the first concave surface and the secondconcave surface.